How does the Ornstein-Uhlenbeck process work, and how it is used in DDPG?
The Ornstein Ulhenebck Process is defined as (in the continuous setting) :
$$dX_t = -\beta(X_t - \alpha)dt + \sigma dW_t$$
The analogue for this process in the discrete time case which I assume will be applicable in the RL case will be:
$$X_{t+1} = X_t -\beta(X_t - \alpha) + \sigma \{W_{t+1}-W_t\}=$$
$$X_{t+1} = (1 -\beta)X_t - \alpha + \sigma \{W_{t+1}-W_t\}$$
In the RL seting the terms in the equation probably means:

$X_t$ will stand for a state in RL i.e. the state is the number $\in \mathbb R$ where the particle moves to at time $t$.
$\beta$ and $\alpha$ are just constants which decide certain movement characteristics of the particle. Check here for graphs plotted for various $\beta$.
$W_t$ is a Weiner process which starts at $W_0 = 0$ and then adds independent increments of $\mathcal N(\mu,\sigma)$ as $W_{t+1} = W_t+\mathcal N(\mu,\sigma)$ which is basically a radom walk. More generally we use $\mathcal N(0,1)$. This is formulated as $W_t-W_s = \sqrt{t-s} \mathcal N(0,1)$. This is because of the fact, $W_t$ can be written recursively as $W_t = \mathcal N(0,1)+W_{t-1} = \mathcal N(0,1) + \mathcal N(0,1) + ...W_s$ and since the samplings are independent at each step the mean get added as $\mu_t+\mu_{t-1}...$ and the variances as $\sigma_t^2 + \sigma_{t-1}^2...$. SInce her the means and variances are $0$ and $1$ respectively, the final mean $\mu = 0$ and variance $\sigma^2 = (t-s)$. And hence, byproperties of Gaussian random variables you can write (it is easy to show this via variable tranformation) $W_t-W_s = \sqrt{t-s} \mathcal N(0,1)$.  Here, is the formulation of standard Weiner process.
$\sigma$ will be the weighting factor of the Weiner process, which just  means the amount of noise being added to the process.

Another useful resource on discrete Ornstein Ulhenbeck process, much less generalized.
I think now you can extend this to whatever scenario you are intereted in RL setting.